Chapter 11.2, Problem 2CFU

To determine

To compare and contract: the graph of $y=b^x$ when $b>1$ and when $0<b<1$ .

Answer to Problem 2CFU

  $\begin{array}{l}\text{decreasing: }0<b<1\\ \text{increasing: }b>1\end{array}$ .

Explanation of Solution

Given:

The graph of $y=b^x$ .

Calculation:

According to the characteristics of given graph, it is concluded that:

  $y=b^x$

the graph of $y=b^x$ are all one to one, have the same domain of all reals, a range of all positive reals, a horizontal asymptote of $y=0$ .

y-intercept of $\left(0,1\right)$ , and no vertical asymptote decreasing when $0<b<1$ and increasing when $b>1$ .

Hence,the given function are all one to one and decreasing when $0<b<1$ and increasing when $b>1$ .